00:01
So you have magdalena a function of x plus 3 over the square root of 2 minus x.
00:12
So you didn't ask a particular question on this, but i'm going to assume that you wanted to know what the domain is in the range.
00:20
So the domain is going to be the set of numbers, and we know that we would need the 2 minus x to be bigger than 0 because it can't equal.
00:30
Zero.
00:31
So that's going to occur when two is bigger than x or when x is less than two.
00:38
So we can write that domain as the set of numbers such that, such that x is less than two, or if you want an interval notation, you would go to negative infinity up to two, like so.
00:54
Now, the range, on the other hand, we know that the denominator, if we plug in numbers that are less than two, the square root of 2 minus x is always going to end up being some type of value that is positive.
01:14
And if we take the numerator of x plus 3, we know that if you plug 2 into this, we can see that that is going to end up being positive values, but you can also get negative values.
01:32
So once you start putting in numbers that are smaller than negative three.
01:37
So the idea is you know you can get positive and negative values from this.
01:43
And notice that the other thing is we would have at, when we plug in negative three, we know we get zero...